(1) Field of Invention
The present invention relates to a system for explosive network attack and mitigation strategies and, more particularly, to a system for explosive network attack and mitigation strategies based on Achlioptas processes.
(2) Description of Related Art
Achlioptas et al. (see the List of Cited Literature References, Literature Reference No. 1) first reported the finding of explosive percolation, where the size of a giant component goes through the first-order phase transition in so called Achlioptas processes. This finding advanced the common belief that the phase transition of a giant component in random network formation is a second-order phenomenon, as demonstrated in the pioneering Erdös-Rényi random graph model (see Literature Reference No. 6). The work of Achlioptas et al. (see Literature Reference No. 1) initiated the interest of the community to actively develop different mechanisms in generating discontinuous phase transitions (see Literature Reference Nos. 3, 4, 5, 8, 9, 10, 11, 13, 14, 17, and 21), as well as develop mathematically rigorous proof about the “discontinuous” phase transition generated by Achlioptas processes (see Literature Reference No. 18). Achlioptas process was later mathematically proven by Literature Reference No. 18 as having continuous transitions when the number of nodes approaches infinity, but having a “weakly” discontinuous property where the simulations up to a 1018-node network so far still show discontinuous phase transitions. Others have used Achlioptas processes to model observed real-world datasets (see Literature Reference Nos. 16 and 19).
Albert et al. (see Literature Reference No. 2) initiated the investigation of system robustness and scale-free complex networks. The major finding was that complex systems with scale-free structures are more resilient to random failures, but fragile to targeted attacks on hub nodes. Literature Reference No. 7 developed theoretical percolation models to characterize network robustness for a wide variety of networks with general degree distributions. The works of Albert et al. (see Literature Reference No. 2) have been applied to the quantification of system robustness for networks including power grids, airlines, Internet, protein-protein interaction networks, neural networks, and many other complex systems.
The most notable recent work includes the demonstration of discontinuous phase transitions of cascading failures between two inter-dependent networks (see Literature Reference No. 6), and the development of a new robustness measure to guide the rewiring of the network to improve system robustness before the attack (see Literature Reference No. 20). Prior works based on Literature Reference Nos. 2 and 7 primarily focused on the quantification of network robustness for a given static network structure without mitigation. The concept of treating mitigation as a competition process amid network attacks or failures is foreign to the community.
Each of the prior methods described above exhibit limitations that make them incomplete. Thus, a continuing need exists for a system that utilizes Achlioptas processes as explosive attack and mitigation strategies to analyze the resilience of complex networks and the effectiveness of mitigations against attacks or failures.